Olympic Measures

8318 /www/nrich/html/content/id/8318/ 1 2012-06-01T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Below are some interesting measurements and records from events at the Olympic Games. Unfortunately they have been muddled up. Can you regroup them correctly? You can print off and cut out <a href="/content/id/8318/Olympic%20Measures%20worksheet.pdf">this set of cards</a>. <table style="border-spacing: 1px; width: 500px; height: 596px" border="1"> <tbody> <tr> <td style="text-align: center;padding:6px;">Usain Bolt's 100 metres World Record</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">seconds</td> </tr> <tr> <td style="text-align: center;padding:6px;">Women's Long Jump World Record</td> <td style="text-align: center;padding:6px;">76.8</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's High Jump World Record</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Basketball hoop diameter</td> <td style="text-align: center;padding:6px;">8.59</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;">Basketball hoop height</td> <td style="text-align: center;padding:6px;">21.3</td> <td style="text-align: center;padding:6px;">inches</td> </tr> <tr> <td style="text-align: center;padding:6px;">Mass of Women's Discus</td> <td style="text-align: center;padding:6px;">1500</td> <td style="text-align: center;padding:6px;">kg</td> </tr> <tr> <td style="text-align: center;padding:6px;">Women's Discus World Record</td> <td style="text-align: center;padding:6px;">01:48:53</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Diameter of Archery target </td> <td style="text-align: center;padding:6px;">6.14</td> <td style="text-align: center;padding:6px;">mph</td> </tr> <tr> <td style="text-align: center;padding:6px;">Archers’ distance from the target</td> <td style="text-align: center;padding:6px;">9.58</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;"> Average speed of World Record Men's 50 km Walking race </td> <td style="text-align: center;padding:6px;">18</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Shot put World Record</td> <td style="text-align: center;padding:6px;">1</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Height of Diving platform</td> <td style="text-align: center;padding:6px;">02:15:25</td> <td style="text-align: center;padding:6px;">feet</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's 10km Swimming 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">cm</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's 50m Swimming 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">7.52</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Paula Radcliffe's Women's Marathon World Record</td> <td style="text-align: center;padding:6px;">122</td> <td style="text-align: center;padding:6px;">km</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Swim (distance)</td> <td style="text-align: center;padding:6px;">23.12</td> <td style="text-align: center;padding:6px;">seconds</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Bicycle ride (distance)</td> <td style="text-align: center;padding:6px;">01:51:52</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Run (distance)</td> <td style="text-align: center;padding:6px;">40</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Triathlon 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">2.45</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Pole Vault World Record</td> <td style="text-align: center;padding:6px;">70</td> <td style="text-align: center;padding:6px;">km</td> </tr> </tbody> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Year 3 at How Wood Primary approached this problem in an interesting way: We tried to work out the problem. We knew we needed to make sensible estimates. To work out Usain Bolt's record, for example, we ran the distance ourselves and found out what times we scored. We thought that he'd be able to do it a little bit faster than us, so that helped make our guesses. Two groups guessed really well with 10 seconds. So we were using what we already know to help us solve a problem. Fantastic! This is a great way to estimate the kinds of numbers you're looking for and use the data you have sensibly. The final table of answers, which loads of people got right, is given below. Thanks to everyone for the submissions! <table style="border-spacing: 1px; width: 500px; height: 596px" border="1"> <tbody> <tr> <td style="text-align: center;padding:6px;">Usain Bolt's 100 metres World Record</td> <td style="text-align: center;padding:6px;">9.58</td> <td style="text-align: center;padding:6px;">seconds</td> </tr> <tr> <td style="text-align: center;padding:6px;">Women's Long Jump World Record</td> <td style="text-align: center;padding:6px;">7.52</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's High Jump World Record</td> <td style="text-align: center;padding:6px;">2.45</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Basketball hoop diameter</td> <td style="text-align: center;padding:6px;">18</td> <td style="text-align: center;padding:6px;">inches</td> </tr> <tr> <td style="text-align: center;padding:6px;">Basketball hoop height</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">feet</td> </tr> <tr> <td style="text-align: center;padding:6px;">Mass of Women's Discus</td> <td style="text-align: center;padding:6px;">1</td> <td style="text-align: center;padding:6px;">kg</td> </tr> <tr> <td style="text-align: center;padding:6px;">Women's Discus World Record</td> <td style="text-align: center;padding:6px;">76.8</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Diameter of Archery target </td> <td style="text-align: center;padding:6px;">122</td> <td style="text-align: center;padding:6px;">cm</td> </tr> <tr> <td style="text-align: center;padding:6px;">Archers’ distance from the target</td> <td style="text-align: center;padding:6px;">70</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;"> Average speed of World Record Men's 50 km Walking race </td> <td style="text-align: center;padding:6px;">8.59</td> <td style="text-align: center;padding:6px;">mph</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Shot put World Record</td> <td style="text-align: center;padding:6px;">23.12</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Height of Diving platform</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's 10km Swimming 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">01:51:52</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's 50m Swimming 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">21.3</td> <td style="text-align: center;padding:6px;">seconds</td> </tr> <tr> <td style="text-align: center;padding:6px;">Paula Radcliffe's Women's Marathon World Record</td> <td style="text-align: center;padding:6px;">02:15:25</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Swim (distance)</td> <td style="text-align: center;padding:6px;">1500</td> <td style="text-align: center;padding:6px;">metres</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Bicycle ride (distance)</td> <td style="text-align: center;padding:6px;">40</td> <td style="text-align: center;padding:6px;">km</td> </tr> <tr> <td style="text-align: center;padding:6px;">Triathlon Run (distance)</td> <td style="text-align: center;padding:6px;">10</td> <td style="text-align: center;padding:6px;">km</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Triathlon 2008 Olympics winner's time</td> <td style="text-align: center;padding:6px;">01:48:53</td> <td style="text-align: center;padding:6px;">hr:min:sec</td> </tr> <tr> <td style="text-align: center;padding:6px;">Men's Pole Vault World Record</td> <td style="text-align: center;padding:6px;">6.14</td> <td style="text-align: center;padding:6px;">metres</td> </tr> </tbody> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3>Why do this problem?</h3> <a href="https://nrich.maths.org/8318">This problem</a> invites students to engage with units of measurement and orders of magnitude, by presenting a variety of records and measurements from events at the Olympic Games. Some will be familiar to students, others may lend themselves to estimation or a little research. <h3>Possible approach</h3> "Here are some interesting measurements and records from events at the Olympic Games. Unfortunately they have been muddled up. Can you regroup them correctly?" Hand out this <a href="/content/id/8318/Olympic%20Measures%20worksheet.pdf">set of cards</a> and invite pairs to work together. If students are stuck, here are some key questions to help them: Which quantities are likely to be whole numbers? Why? Which quantities are lengths? Which are times? Which are speeds? Which are masses? Which units might belong with the lengths... times... speeds... masses...? Can you rank the different lengths... times... speeds... masses in order of magnitude? Finish by bringing the whole class together to agree on a class ordering for the cards. Students will need to convince each other of their own ordering by explaining what they are certain of, and justifying their educated guesses. The videos of impressive world record performances available on <a href="http://listverse.com/2007/10/02/top-10-impressive-athletics-world-records/">this site</a> might be of interest to students. (Link is to an external site, NRICH is not responsible for the contents.) One teacher created a PowerPoint to use with this task; you can download it from the <a href="http://www.tes.co.uk/teaching-resource/Olympic-Measures-ppt-for-nrich-activity-6256165/">TES Resources</a> website. <h3>Possible extension</h3> Invite students to do some research to create a set of similar cards of their own to swap with a friend. Students could also have a go at <a href="/5994">All in a Jumble</a> where the measurements have again been all jumbled up. <h3>Possible support</h3> This <a href="/content/id/8318/Olympic%20Measures%20Support.pdf">set of cards</a> only requires students to sort the measurements, as the units are included with each quantity. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Which quantities are times? Which are speeds? Which are distances? There are some standard quantities, and some world records or times. Think about whether each of these is likely to be a whole number or a decimal. Once you've identified all the distances, try ranking them in order of magnitude.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Top 10 Impressive Athletics World Records: http://listverse.com/2007/10/02/top-10-impressive-athletics-world-records/ <a href="/content/id/8318/Olympic%20Measures%20Answers.pdf">Olympic Measures Answers.pdf</a></mdoxml> 2 3 0 0 1 0 0 Olympic Measures These Olympic quantities have been jumbled up! Can you put them back together again? Applications Maths Supporting SET Applications sport Measures and Mensuration Metric units Measures and Mensuration Imperial units Measures and Mensuration Length/distance Secondary Mapping Document Units of measurement Secondary Mapping Document DisplayCabinet